Inner models in the region of a Woodin limit of Woodin cardinals Original Research Article

We extend the construction of Mitchell and Steel (Fine Structure and Iteration Trees, Lecture Notes in Logic, vol. 3, Springer, Berlin, 1994) to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more. The precise level reached is that of a cardinal which is both a Woodin cardinal and a limit of cardinals strong past it.